为什么这个二进制搜索函数的下界是最大值而不是最小值？

Question

下面的代码是二进制搜索函数的一个较大的二进制搜索问题。你知道吗

我的理解是，下界应该是排序数组中的最小值，而上界应该是最高索引（或最大值）。为什么在这种情况下使用max()和sum()？你知道吗

def binarySearch(A, max_block_cnt, M):
    lower_bound = max(A)
    upper_bound = sum(A)

    if max_block_cnt == 1:      return upper_bound
    if max_block_cnt >= len(A): return lower_bound

    while lower_bound <= upper_bound:
        candidate_mid = (lower_bound + upper_bound) // 2
        if blockSizeIsValid(A, max_block_cnt, candidate_mid):
            upper_bound = candidate_mid - 1
        else:
            lower_bound = candidate_mid + 1

    return lower_bound  

这个问题就是MinMaxDivision问题。如果需要更多细节，请告诉我。你知道吗

编辑--显示所需的更多信息。下面是我正在研究的问题：

You are given integers K, M and a non-empty zero-indexed array A consisting of N integers. Every element of the array is not greater than M.

You should divide this array into K blocks of consecutive elements. The size of the block is any integer between 0 and N. Every element of the array should belong to some block.

The sum of the block from X to Y equals A[X] + A[X + 1] + ... + A[Y]. The sum of empty block equals 0.

The large sum is the maximal sum of any block.

For example, you are given integers K = 3, M = 5 and array A such that:

A[0] = 2 A[1] = 1 A[2] = 5 A[3] = 1 A[4] = 2 A[5] = 2
A[6] = 2 The array can be divided, for example, into the following blocks:

[2, 1, 5, 1, 2, 2, 2], [], [] with a large sum of 15; [2], [1, 5, 1, 2], [2, 2] with a large sum of 9; [2, 1, 5], [], [1, 2, 2, 2] with a large sum of 8; [2, 1], [5, 1], [2, 2, 2] with a large sum of 6. The goal is to minimize the large sum. In the above example, 6 is the minimal large sum.

Write a function:

def solution(K, M, A)

that, given integers K, M and a non-empty zero-indexed array A consisting of N integers, returns the minimal large sum.

For example, given K = 3, M = 5 and array A such that:

A[0] = 2 A[1] = 1 A[2] = 5 A[3] = 1 A[4] = 2 A[5] = 2
A[6] = 2 the function should return 6, as explained above.